I try to go back to the original question, how can I measure the wire with that precision ?
I don't think there is a practical mechanical way to achieve such precision.
So what about a digital microscope ?
well I don't know your budget (there are cheaper options), but the idea is to "enlarge" the wire, and measure the variation of the image. I mean, measure the difference of light transmittance .....
Maybe it's just an weird idea but I have no other.